Transistor based PUF apparatus

ABSTRACT

The present disclosure relates to a PUF apparatus and method for generating a persistent, random number. The generated number is random in that each particular instance of PUF apparatus should generate a randomly different number to all other instances of PUF apparatus, and is persistent in that each particular instance of the PUF apparatus should repeatedly generate the same number, within acceptable error correction tolerances. The persistent, random number is determined by selecting one or more PUF cells, each comprising a matched pair of transistors that are of identical design, and comparing an on-state characteristic of the pair (e.g., turn-on threshold voltage or gate-source voltage). The difference in on-state characteristic of each selected pair of transistors is caused by random manufacturing differences between the transistors. This causes the randomness between each different instance of PUF apparatus, and should be relatively stable over time to provide persistence of the generated number.

TECHNICAL FIELD

The present disclosure relates to transistor based, physical unclonablefunction (PUF).

BACKGROUND

A physical unclonable function or ‘PUF’ is a physical entity capable ofgenerating an output (‘response’) to a given input (‘challenge’) that isunique to that particular PUF such that it can be regarded as a‘fingerprint’. This capacity is typically arrived at by devising the PUFin such a way that its output depends upon features that differ randomlyin each device due to minor manufacturing variations. Thus, a PUF cannotbe readily replicated with the correct fingerprint, even with fullknowledge of its circuit layout. The response may be used for variousdifferent purposes, for example in cryptographic operations to securecommunications to/from a device that includes the PUF, or used in aprocess of authenticating the identity of a device that includes thePUF, etc.

SUMMARY

The present disclosure relates to a PUF apparatus for generating apersistent, random number. The number is random in that each particularinstance of the PUF apparatus should generate a randomly differentnumber to all other instances of the PUF apparatus, and is persistent inthat each particular instance of the PUF apparatus should repeatedlygenerate the same number, within acceptable error correction tolerances.The random number is determined by selecting one or more PUF cells, eachof which comprise a matched pair of transistors that are of identicaldesign, and then comparing an on-state characteristic of the pair, suchas turn-on threshold voltage or gate-source voltage. The difference inon-state characteristic of each selected pair of transistors is causedby random manufacturing differences between the transistors, whichcreates the randomness between each different instance of PUF apparatus,and which should be relatively stable over time which contributes to thepersistence of the generated number.

A PUF apparatus may comprise one or more PUF cells, each comprising somephysical features that differ randomly in each device due to minormanufacturing variations, and some determination circuitry configured toreadout a PUF value from each of the PUF cells. The PUF apparatus may beconfigured such that the determination circuitry can read out a randomPUF value from each of the PUF cells and generate a persistent randomnumber based on the PUF value(s). The persistent random number may thenbe used as part of the determination of a ‘response’ to a ‘challenge’.For example, the PUF apparatus may receive a ‘challenge’ from anothercircuit, the determination circuitry may then read the persistent randomnumber from the PUF cells and the PUF apparatus may then determine a‘response’ based on the ‘challenge’ and the persistent random number(for example, but carrying out some cryptographic operation, such as ahash, or XOR, or encryption using the ‘challenge’ and the persistentrandom number). A persistent random number is random in that its valueis dependent on the minor, random manufacturing variations betweendifferent PUF apparatus. Thus, different instances of the PUF apparatus,whilst identical in design, should each generate a different, persistentrandom number. A random number is ‘persistent’ in that it should staythe same, or stay the same within acceptable limits, over time. Forexample, the persistent random number generated by the one or more PUFcells of a PUF apparatus should be the same each time it is generated(or stay the same within acceptable limits, for example so that it canbe corrected using error correcting code, ECC), so that it can act as areliable fingerprint of the device.

In a first aspect of the present disclosure, there is provided aPhysically Unclonable Function, PUF, apparatus comprising: a pluralityof PUF cells, each PUF cell comprising: a plurality of transistors,wherein the plurality of transistors comprises: a matched pair oftransistors for transistor on-state characteristic comparison, and aselection mechanism for selecting the PUF cell, and wherein theplurality of transistors in each PUF cell are all of the same transistortype; and a determination unit configured to: select at least one of theplurality of PUF cells using the selection mechanism in each of the atleast one of the plurality of PUF cells; for each selected PUF cell,determine a transistor difference value based at least in part on acomparison of an on-state characteristic of the matched pair oftransistors in the selected PUF cell, wherein the transistor differencevalue is indicative of a random manufacturing difference between thematched pair of transistors in the selected PUF cell; and determine aPUF output based at least in part on the at least one determinedtransistor difference value.

The selection mechanism may comprise gate terminals of the pair oftransistors, and wherein the determination unit is configured to selecta PUF cell by applying a selection potential to one or more of the gateterminals of the matched pair of transistors in the PUF cell.

The selection mechanism may comprise one or more selection transistorscoupled to the matched pair of transistors, and wherein thedetermination unit is configured to select a PUF cell by applying aselection potential to the one or more selection transistors to controlan operation of the one or more selection transistors.

The comparison of the on-state characteristic of the matched pair oftransistors may comprise a comparison of a gate-source voltage of thematched pair of transistors.

The determination unit may be configured to determine the transistordifference value for a selected PUF cell by: (a) applying a first inputsignal to a first transistor of the matched pair of transistors;applying a second input signal to a second transistor of the matchedpair of transistors; and determining a first transistor comparison valueby comparing the on-state characteristic of the first transistor whenthe first input signal is applied against the on-state characteristic ofthe second transistor when the second input signal is applied; then (b)applying the second input signal to the first transistor of the matchedpair of transistors; applying the first input signal to the secondtransistor of the matched pair of transistors; and determining a secondtransistor comparison value by comparing the on-state characteristic ofthe first transistor when the second input signal is applied against theon-state characteristic of the second transistor when the first inputsignal is applied; and then (c) determining the transistor differencevalue based on the first transistor comparison value and the secondtransistor comparison value (for example, based on a sum, or an averageor a difference of the first and second transistor comparison values).

The determination unit (170) may be configured to: in (a),simultaneously apply the first input signal to the first transistor andthe second input signal to the second transistor; and in (b),simultaneously apply the second input signal to the first transistor andthe first input signal to the second transistor.

The determination unit (170) may further comprise: at least one firstcurrent source (232 _(x)) configured to output a first current signal;and a second current source (234 _(x)) configured to output a secondcurrent signal; wherein the first input signal comprises the firstcurrent signal and the second input signal comprises the second currentsignal.

The first input signal may comprise a first voltage signal and thesecond input signal comprises a second voltage signal.

The at least one of the first voltage signal and the second voltagesignal may vary with time.

The determination unit may be configured to: during determination of thefirst transistor comparison value for a selected PUF cell, apply thefirst voltage signal to a gate terminal of the first transistor andapply the second voltage signal to a gate terminal of the secondtransistor; and during determination of the second transistor comparisonvalue for a selected PUF cell, apply the second voltage signal to thegate terminal of the first transistor and apply the first voltage signalto the gate terminal of the first transistor so as also to select thePUF cell.

The selection mechanism may comprise the gate terminals of the matchedpair of transistors, and wherein the first voltage signal and the secondvoltage signal also act as selection potentials for selecting the PUFcell.

The matched pair of transistors may be configured as a differentialpair, and wherein the matched pair of transistors form an input of acomparator.

The transistor difference value may comprise a digital value indicativeof the random manufacturing difference between the matched pair oftransistors, and wherein the determination unit comprises anAnalog-to-Digital converter for use in determining the transistordifference value, and wherein the Analog-to-Digital converter comprisesthe comparator.

Each matched pair of transistors may comprise a first transistor and asecond transistor, and wherein the first transistor comprises a firstsub-transistor and a second sub-transistor, and wherein the secondtransistor comprises a third sub-transistor and a fourth sub-transistor,and wherein the first sub-transistor, second sub-transistor, thirdsub-transistor and fourth sub-transistor are arranged in a semiconductorlayout such that a centre of mass of the first transistor issubstantially the same as a centre of mass of the second transistor.

The first sub-transistor, the second sub-transistor, the thirdsub-transistor and the fourth sub-transistor may be arranged in asemiconductor layout such that: when the first transistor is conductingcurrent, a channel current in the first sub-transistor flows in a firstdirection in the semiconductor and a channel current in the secondsub-transistor flows in a second direction in the semiconductor, andwhen the second transistor is conducting current, a channel current inone of the third sub-transistor and the fourth sub-transistor flows inthe first direction and a channel current in the other of the thirdsub-transistor and the fourth sub-transistor flows in the seconddirection, and wherein the first direction and the second direction aresubstantially opposite spatial directions in the semiconductor layout

A semiconductor layout of the matched pair of transistors may bearranged such that the first sub-transistor and third sub-transistorshare a drain terminal and the second sub-transistor and the fourthsub-transistor share a further drain terminal.

In a second aspect of the disclosure, there is provided a method fordetermining a Physically Unclonable Function, PUF, output using aplurality of PUF cells each comprising a plurality of transistors of thesame transistor type, the plurality of transistors comprises a matchedpair of transistors and a selection mechanism for selecting the PUFcell, the method comprising: selecting one or more PUF cells using theselection mechanism in each of the at least one of the plurality of PUFcells (105 _(x,y)); for each selected PUF cell, determining a transistordifference value based at least in part on a comparison of an on-statecharacteristic of the matched pair of transistors in the selected PUFcell, wherein the transistor difference value is indicative of a randommanufacturing difference between the matched pair of transistors in theselected PUF cell; and determining the PUF output based at least in parton the at least one determined transistor difference value.

Determining the transistor value for a selected PUF cell may comprise:applying a first input signal and a second input signal to a firsttransistor of the matched pair of transistors and a second transistor ofthe matched pair of transistors respectively; determining a firsttransistor comparison value by comparing the on-state characteristic ofthe matched pair of transistors; applying the first input signal and thesecond input signal to the second transistor and the first transistorrespectively; determining a second transistor comparison value bycomparing the on-state characteristic of the matched pair oftransistors; and determining the transistor difference value based on adifference between the first transistor comparison value and the secondtransistor comparison value.

The first input signal may comprise a first current and/or a firstvoltage signal, and the second input signal may comprise a secondcurrent and/or a second voltage signal.

Selecting a PUF cell may comprise applying a selection potential to oneor more of the gate terminals of the matched pair of transistors in thePUF cell.

In a third aspect of the disclosure, there is provided an apparatus (forexample, a PUF apparatus) comprising: a pair of transistors comprising:a first transistor; and a second transistor coupled to the firsttransistor to form the pair of transistors, wherein the first transistorcomprises a first sub-transistor and a second sub-transistor, andwherein the second transistor of the pair of transistors comprises athird sub-transistor and a fourth sub-transistor.

The first sub-transistor, second sub-transistor, third sub-transistorand fourth sub-transistor may be arranged in a semiconductor layout suchthat a centre of mass of the first transistor is substantially the sameas a centre of mass of the second transistor.

A semiconductor layout of the pair of transistors may be arranged suchthat the first sub-transistor and third sub-transistor share a drainterminal and the second sub-transistor and the fourth sub-transistorshare a further drain terminal.

The first sub-transistor, the second sub-transistor, the thirdsub-transistor and the fourth sub-transistor may be arranged in asemiconductor layout such that: when the first transistor is conductingcurrent, a channel current in the first sub-transistor flows in a firstdirection in the semiconductor and a channel current in the secondsub-transistor flows in a second direction in the semiconductor, andwhen the second transistor is conducting current, a channel current inone of the third sub-transistor and the fourth sub-transistor flows inthe first direction and a channel current in the other of the thirdsub-transistor and the fourth sub-transistor flows in the seconddirection, and wherein the first direction and the second direction aresubstantially opposite spatial directions in the semiconductor layout.

The apparatus may further comprise: a further pair of transistors havingthe same semiconductor design as that of the pair of transistors,wherein the pair of transistors and the further pair of transistors arearranged in the semiconductor layout such that the second sub-transistorof the pair of transistors and a first sub-transistor of the furtherpair of transistors share a source terminal.

The drain terminal of the first transistor of the pair of transistorsand a drain terminal of a first transistor of the further pair oftransistors may be coupled to a first common signal output line, andwherein the drain terminal of the second transistor of the pair oftransistors and a drain terminal of the first transistor of the furtherpair of transistors may be coupled to a second common signal outputline.

The apparatus may further comprise an even further pair of transistors,wherein the apparatus comprises: a first gate structure forming a gatefor the first transistor of the pair of transistors and a firsttransistor of the even further pair of transistors, such that a gatepotential for the first transistor of the pair of transistors issubstantially the same as a gate potential for the first transistor ofthe even further pair of transistors; and a second gate structureforming a gate for the second transistor of the pair of transistors anda second transistor of the even further pair of transistors, such that agate potential of the second transistor of the pair of transistors issubstantially the same as a gate potential of the second transistor ofthe even further pair of transistors.

The first transistor and the second transistor may be MOS devices (forexample, PMOS devices).

The apparatus may further comprise a plurality of pairs of transistorsarranged in a two-dimensional array.

DRAWINGS

Aspects of the present disclosure are described, by way of example only,with reference to the following drawings, in which:

FIG. 1 shows an example schematic representation of PUF apparatus inaccordance with an aspect of the present disclosure;

FIG. 2 shows an example schematic representation of an implementation ofa PUF cell and determination unit of the PUF apparatus of FIG. 1;

FIG. 3 shows an example schematic representation of an array of the PUFcells of FIG. 2;

FIG. 4 shows an example schematic representation of a furtherimplementation of a PUF cell and determination unit of the PUF apparatusof FIG. 1;

FIG. 5 show a graphic representing operational signals in the of the PUFapparatus of FIG. 4;

FIG. 6 shows an example schematic representation of an array of the PUFcells of FIG. 4;

FIG. 7 shows an example schematic representation of a furtherimplementation of a PUF cell and determination unit of the PUF apparatusof FIG. 1;

FIG. 8 shows a schematic diagram illustrating a pair of transistors anda partial comparator block;

FIG. 9 shows an example representation of an array of PUF cellscomprising the pair of transistors of FIG. 8 and a determination unitcomprising the partial comparator block of FIG. 8;

FIGS. 10A-10D show an example schematic representation of an arrangementof a pair of transistors;

FIG. 11A shows an example schematic representation of a pair oftransistors;

FIG. 11B shows an example schematic representation of the pair oftransistors of FIG. 11A implemented by sub-transistors;

FIG. 12 shows an example semiconductor layout of the sub-transistors ofFIG. 11B;

FIG. 13 shows an example schematic representation of an array of thesemiconductor layout of FIG. 12;

FIG. 14 shows an example schematic representation of a PUF cellcomprising a pair of transistors and a separate selection mechanism;

FIG. 15 shows an example schematic representation of a furtherimplementation of a PUF cell;

FIG. 16 shows an example schematic representation of a furtherimplementation of a PUF cell; and

FIG. 17 shows a graphical representation of a method for determining aPUF output using a plurality of PUF cells.

DETAILED DESCRIPTION

The inventors have identified many different challenges in implementinga PUF apparatus with one or more PUF cells. First, each possible outputof a PUF cell should have an equal, or substantially equal, probability.For example, if a PUF cell is configured to output a ‘1’ or a ‘0’depending on random manufacturing variations the PUF cell, there shouldbe an equal, or substantially equal, probability of a ‘1’ or a ‘0’. Ifthis is not achieved, the output of the PUF cell may not be sufficientlyrandom. Achieving this requires a circuit design and layoutconfiguration of each PUF cell, and the PUF apparatus overall, that willnot favour any one particular possible output value.

Second, it is preferable for the PUF apparatus to be low cost, in termsof power consumption and/or area used in an integrated circuit (IC)and/or time required to generate the PUF output, so that it can beimplemented in devices more easily. For example, PUF apparatus may beparticularly useful for Internet of Things (IoT) device security, suchas for authenticating the identity of an IoT device and/or securingcommunications to/from an IoT device. In order to include a PUFapparatus in an IoT device, it is helpful for the PUF apparatus to becheap and/or low power and/or small.

To address at least some of these challenges, a PUF apparatus isdisclosed herein, which comprises a plurality of PUF cells 105 _(x,y).Each of the PUF cells includes a plurality of transistors 210 _(x,y)that are all of the same transistor type, and include a selectionmechanism and a matched pair of transistors 210 _(x,y). The matched pairof transistors are identical in design, but will inherently have somerandom manufacturing differences, which should result in differences intheir on-state characteristics. One or more particular PUF cells can beselected for measurement using their selection mechanism and adifference between an on-state characteristic, such as gate-sourcevoltage, for the matched pair of transistors in the selected cell(s)determined. Based on the comparison of the on-state characteristic ofone or more PUF cells, a persistent random number can be generated asthe PUF output.

By making the plurality of transistors in each cell of the same type(for example, all p-type, or all n-type), it is possible to make eachPUF cell to a very small dimension, which can this increase the densityof the PUF cells and thereby reduce the overall size of the PUFapparatus. In addition to this, the reduction of size may improve therandomness in the transistor on-state characteristic of each cell, bymitigating any bias towards one transistor or the other caused bygradients, such as doping gradients or oxide gradients, across the cell.Furthermore, by comparing the on-state characteristics of the matchedpair of transistors (as opposed to failure characteristics, forexample), reliability may be improved since high voltages are notapplied and gate oxides are not degraded, and the pair of transistorsmay be used for additional purposes, such as acting as the selectionmechanism, thereby even further reducing the size of each cell.

FIG. 1 shows an example schematic representation of PUF apparatus 100 inaccordance with an aspect of the present disclosure. The PUF apparatuscomprises a plurality of PUF cells 105 _(x,y), a determination unit 170and a challenge/response unit 180. Whilst only a 2×2 array of PUF cells105 _(x,y) is represented, it will be appreciated that there may be anynumber of PUF cells, (for example, 8, 12, 20, 32, 128, 256, etc, etc)arranged in an array of any size and dimension, or arranged in any othersuitable configuration.

The determination unit 170 is configured to determine a PUF output usingthe plurality of PUF cells 105 _(x,y). The PUF output is a persistentrandom number, which is explained in more detail in the ‘background’section of this disclosure.

The challenge/response unit 180 is configured to receive a ‘challenge’from an external entity, request and obtain the PUF output from thedetermination unit 170 and then determine and return a response based onthe challenge and the PUF output. The challenge/response unit 180 may beconfigured to operate in any suitable way that will be apparent to theperson skilled in the art of PUF devices. The challenge/response unit180 may form a separate unit, or may be part of the determination unit170. The present disclosure is concerned specifically with theconfiguration and operation of the PUF cells 105 _(x,y) anddetermination unit 170, as described in detail below. Therefore, nofurther reference to, or explanation of, the challenge/response unit 180is given in this disclosure.

FIG. 2 shows a schematic diagram of an example implementation of a PUFcell 105 and the determination unit 170 configured to determine a PUFvalue of the PUF cell 105.

FIG. 3 shows a schematic diagram of an array of PUF cells 105 _(x,y)that are each configured in the same way as the PUF cell 105 representedin FIG. 2.

Returning to FIG. 2, the PUF cell 105 comprises a matched pair oftransistors 210. The term ‘matched’ in this disclosure means that thepair of transistors are of identical design. Whilst FIG. 2 shows arepresentation of a matched pair of p-type FETs, it will be appreciatedthat throughout the present disclosure, in every different describedaspect, the matched pair of transistors 210 may be of any transistortype, for example p-type, n-type, enhancement, depletion, FETs (such asMOSFETs, JFETs, MESFETs, etc), BJTs (such as IGBTs, heterojunctionbipolar transistors, etc), etc. For the sake of simplicity, thisdisclosure focuses specifically on FETs, but it should be appreciatedthat the terms ‘gate’, ‘source’ and ‘drain’ used herein encompass theterms ‘base’, ‘emitter’ and ‘collector’ of BJTs.

Whilst the two transistors making up the matched pair of transistors 210are of identical design, in practice there will inevitably be small,random manufacturing variations between the two transistors. Thosemanufacturing variations may include at least one of: differences ingate oxide thickness, differences in doping densities, differences incarrier mobility, differences in device dimensions, etc. Thesemanufacturing variations result in variations in transistor on-statecharacteristics/performance, such as differences in turn-on thresholdvoltage, differences in β, differences in the back-gate effect, etc. Theterm ‘on-state’ is used throughout this disclosure to refer to anoperational characteristic of a transistor relating to its normal onstate operation, such as turn-on threshold voltage, gate-source voltage,drain current, linear resistivity, saturation point, transconductance,etc. By considering an on-state characteristic, as opposed to anoff-state characteristic (such as off-state leakage current) or afailure characteristic (such as dielectric breakdown), reliability ofthe PUF apparatus 100 may be increased, since high voltages are notapplied, gate oxides are not degraded, etc. Furthermore, the matchedpair of transistors 210 may be used for other purposes in addition tothe characteristic comparison, such as forming part of a selectionmechanism (as explained later).

The determination unit 170 is configured to determine a transistordifference value based at least in part on a comparison of an on-statecharacteristic of the matched pair of transistors 210, wherein thetransistor difference value is indicative of one or more randommanufacturing differences between the matched pair of transistors 210.In this implementation, the compared on-state characteristic of thematched pair of transistors 210 is the gate-source voltage of the twotransistors (V_(GS)). The V_(GS) of the two transistors may differ as aresult of one or many different random manufacturing differences thatcause, for example, a difference in the turn-on threshold voltage and/orβ and/or back-gate effect, of the transistors.

The drains of the matched pair of transistors 210 are coupled to ground.The determination unit 170 comprises a selector circuit 220 configuredto apply a suitable voltage to the gates of the matched pair oftransistors 210 in order to turn-on the transistors. This voltagefunctions as a ‘selection potential’, which is explained in more detailbelow with reference to FIG. 3 The determination unit 170 also comprisesa first current source 232 and a second current source 234, that areconfigured to provide the same amount of current as each other. Thecurrent from the first current source 232 may be applied as a firstinput signal to the source of a first transistor of the matched pair oftransistors 210, and the current from the second current source 234 maybe applied as a second input signal to the source of a second transistorof the matched pair of transistors 210. If the matched pair oftransistors 210 were truly identical, their source voltages would beexactly the same. However, owing to random manufacturing differences,the gate-source voltages of the two transistors are likely to bedifferent and, since the gate voltage applied to the matched pair oftransistors 210 is the same, the source voltages of the matched pair oftransistors 210 should be different by some amount.

The determination unit 170 further comprises an ADC 250 that isconfigured to measure the difference in the gate-source voltage andoutput a digital value indicative of the difference. However, it hasbeen realised that there may be some mismatch between the currentsprovided by the first current source 232 and the second current source234. Therefore, a chop circuit 236 may be provided so that the firstinput signal (the current from the first current source 232) may beapplied to the first transistor, the second input signal (the currentfrom the second current source 234) may be applied to the secondtransistor and a first transistor comparison value determined by the ADC250 by comparing the gate-source voltages of the matched pair oftransistors 210. Then, the chop circuit 236 may switch the coupling ofthe first current source 232 and the second current source 234 such thatthe first input signal is applied to the second transistor, the secondinput signal is applied to the first transistor and a second transistorcomparison value is determined by the ADC 250 by comparing thegate-source voltages of the matched pair of transistors 210.

The first and second transistor comparison values may be expressed as:First transistor mismatch value=ΔV _(GS)+mismatch+noise1Second transistor mismatch value=ΔV _(GS)−mismatch+noise 2

The transistor difference value for the PUF cell 105 may then bedetermined based on the first transistor comparison value and the secondtransistor comparison value, for example from a sum or an average of thefirst transistor comparison value and the second transistor comparisonvalue.

For example, the transistor difference value may be expressed as:transistor difference value=first mismatch value+second mismatchvalue=2*ΔV _(GS)+noise1+noise2Ortransistor difference value=avg of first mismatch value and secondmismatch value=ΔV _(GS)+(noise1+noise2)/2

In this way, any measurement inaccuracies caused by a mismatch betweenthe first and second current sources 232 and 234 may be significantlyreduced or eliminated to the first order. Furthermore, the signal tonoise ratio may also be improved, in general by about √2, since noise1and noise2 are largely uncorrelated. It will be appreciated that thechop circuit 236 is optional and the determination unit 170 may beconfigured to determine the transistor difference value from a singlecomparison of the gate-source voltages, for example if the first andsecond current sources are considered to be matched to a sufficientlyhigh accuracy.

Furthermore, optionally, a further chop circuit 240 may be provided atthe input to the ADC 250. This may operate similarly to the chop circuit236, and at the same time as the chop circuit 236, in order to switchthe coupling of differential inputs to a comparator in the ADC 250. Inthis case however, the sign of the ΔV_(GS) component in the firsttransistor comparison value will be different from the sign of theΔV_(GS) component in the second transistor comparison value as a resultof switching the inputs to the comparator in the ADC 250. For example,in the case where both chop circuit 236 and 240 are used:First transistor mismatch value=ΔV _(GS)+mismatch+offset+noise1Second transistor mismatch value=−ΔV _(GS)+mismatch+offset+noise 2where offset is the offset of the ADC 250.

In this case, the transistor difference value may be determined bytaking the difference of the first transistor comparison value and thesecond transistor comparison value. For example:transistor difference value=first mismatch value−second mismatchvalue=2*ΔV _(GS)+noise1−noise2

Using the chop circuit 236 in this way may help to cancel any offset inthe ADC 250 and well as any mismatch between the first and secondcurrent sources 232 and 234. Furthermore, the ΔV_(GS) component hasincreased by 2× and low frequency components of noise1 and noise2 shouldmostly cancel each other out. However, it will be appreciated that thechop circuit 240 is optional, depending on the configuration of the ADC250 and the quality of components making up the ADC 250. Furthermore,the determination unit 170 may not comprise an ADC 250, but may insteaddetermine the transistor difference value using any other suitablecircuitry, for example analog only circuitry.

The chop circuit 236 and further chop circuit 240 may be configured inany suitable way to perform the switching/chopping functionalitydescribed above. For example, they may each comprise one or moreswitches that can be controlled (for example, by a control unit notrepresented in FIG. 2) to switch/chop the couplings as described above.

The transistor difference value is indicative of which of thetransistors in the matched pair of transistors 210 has thelarger/smaller V_(GS). For example, it may simply be a “1” if the V_(GS)of the first transistor is larger than the V_(GS) of the secondtransistor, and a “0” if the V_(GS) of the first transistor is smallerthan the V_(GS) of the second transistor. Alternatively, it may also beindicative of the magnitude of the difference. For example, it may be apositive number of a magnitude indicative of the amount by which theV_(GS) of the first transistor is larger than the V_(GS) of the secondtransistor, and may be a negative number of a magnitude indicative ofthe amount by which the V_(GS) of the first transistor is smaller thanthe V_(GS) of the second transistor.

Turning to FIG. 3, a plurality of PUF cells 105 _(x,y) are represented,where x=1, 2, . . . X−1, X and y=1, 2, . . . Y−1, Y, such that theoverall number of PUF cells 105 _(x,y) totals X*Y. The PUF cells 105_(x,y) in this example are arranged in an array comprising X columns andY rows. The selector circuit 220 has Y outputs, one for each row of thearray and it can be seen that each output is coupled to the gates of allof the matched transistor pairs 210 _(x,y) in a particular row (forexample, the first output is coupled to transistor pairs 210 _(x,1), thesecond output is coupled to transistor pairs 210 _(x,2), etc). In orderto select a particular row of PUF cells 105 _(x,y), the selector circuit210 applies a selection potential to that row (for example, a potentialthat exceeds the turn-on threshold voltage of the transistors) in orderto turn on the matched transistor pairs 210 _(x,y) in that row. Anon-selection potential is applied to all other rows (for example, apotential that is less than the turn-on threshold voltage of thetransistors). Thus, it can be seen that in this example, each matchedtransistor pair 210 _(x,y) is not only used for determining a transistordifference value, it is also used as a selection mechanism for its PUFcell 105 _(x,y). By using each matched pair of transistors 210 _(x,y)for both of these purposes, the size of the PUF cell array may bereduced compared with an array that includes a pair of transistors to beused for the determination of a PUF value, and one or more furthertransistors to be used to select a PUF cell.

It can also be seen that the determination unit 170 comprises X firstand second current sources 232 _(x) and 234 _(x), X chop circuits 236_(x), X further chop circuits 240 _(x) and X ADCs 250 _(x).Consequently, it is possible to determine, in parallel, transistordifference values for the X pairs of transistors 210 _(x,y) in aselected row, thereby increasing the speed of operation. Furthermore,each set of first and second current sources 232 _(x) and 234 _(x), chopcircuit 236 _(x), further chop circuit 240 _(x) and ADC 250 _(x) may beshared by a column of the PUF array, thereby reducing the number ofcomponents required and thus the overall size, cost and powerconsumption of the PUF apparatus 100.

The determination unit 170 represented in FIG. 3 also comprises a PUFoutput unit 310 that either: a) receives the determined transistordifference value from each ADC 250 _(x), or b) receives the determinedfirst and second transistor comparison values from each ADC_(x) and thendetermines the transistor difference value based on the first and secondtransistor comparison values (for example, by averaging them).

The determination unit 170 may operate by selecting one row of PUF cells105 _(x,y) and determining a transistor difference value for eachselected PUF cell. Subsequently, the next row of PUF cells 105 _(x,y)may be selected and transistor difference values determined for them.The operation of the selector circuit 220, chop circuits 236 _(x) andfurther chop circuits 240 _(x) may be controlled in any suitable way,for example by the PUF output unit 310 or any other suitable controller.Control interconnections are not represented in FIG. 3 for the sake ofsimplicity.

The PUF output determined by the PUF output unit 310 is a persistentrandom number that may be, for example, a multi-bit number. For example,if the PUF apparatus 100 is configured such that each PUF cell 105_(x,y) is used to determine the value of one bit of the multi-bit PUFoutput, if there are 128 PUF cells 105 _(x,y) the output unit 310 maygenerate a 128-bit PUF output, where the transistor difference value foreach PUF cell 105 _(x,y) determines the value of each bit (i.e., either“0” or “1”). For example, if the transistor difference value determinedfor a particular PUF cell 105 _(x,y) is indicative of the V_(GS) of thefirst transistor being greater than the V_(GS) of the second transistor,the corresponding bit in the PUF output may be set to 1. If it isindicative of the V_(GS) of the first transistor being less than theV_(GS) of the second transistor, the corresponding bit in the PUF outputmay be set to 0. Since the outcome of each transistor comparison isdependent on random manufacturing differences between the matched pairof transistors 210 _(x,y), it can be seen that the PUF output should berandom, in that each different instance of PUF apparatus 100 is highlylikely to generate a randomly different PUF output. Furthermore, theoutcome of each transistor comparison should generally stay the sameover time (i.e., if V_(GS) of the first transistor is determined to beless than V_(GS) of the second transistor, this should not change overtime) or stay the same to within acceptable limits (for example, achange for a small number of matched transistor pairs 105 _(x,y) may beacceptable, since it may be possible for ECC to correct for thosechanges), such that the PUF output is persistent.

In some implementations, the number of PUF cells 105 _(x,y) may exceedthe number of bits in the PUF output. In this case, during enrolment ofthe PUF apparatus 100, the transistor comparison described above may becarried out for all of the PUF cells 105 _(x,y). The PUF cells 105_(x,y) that are found to have the largest difference in V_(GS) in theirmatched pair of transistors 210 _(x,y) may then be registered for use indetermining the PUF output in the future. The remaining PUF cells 105_(x,y) may effectively be ignored from then on. By using only the PUFcells 105 _(x,y) with the largest difference in V_(GS), the persistenceof the PUF output may be improved, since changes over time in themagnitude of a difference in the transistor on-state characteristic (forexample, caused by component drift, measurement noise, etc) are lesslikely to cause a change in which of the two transistors has the largestV_(GS).

Whilst the above focuses specifically on the comparison of V_(GS), itwill be appreciated that other transistor on-state characteristics maybe compared in accordance with the present disclosure.

FIG. 15 shows an example configuration of a PUF cell 105 where thecompared transistor on-state characteristic is channel, or drain,current I_(D). In this arrangement, the matched pair of transistors 210may be selected by the selector circuit 220, as described above withreference to FIGS. 2 and 3 and they may share a single current source1510. If the matched pair of transistors 210 were perfectly identical,the channel current I_(D1) through the first transistor of the pairwould be identical to the channel current I_(D2) through the secondtransistor of the pair. However, owing to random manufacturingdifferences, there is likely to be a difference between I_(D1) andI_(D2). The determination unit 170 comprises a current measurement unit1520 configured to measure the difference between the currents, based onwhich the PUF output can be determined (similarly to the descriptionabove with reference to FIG. 3). Optionally, the determination unit 170may comprise the chop 240 so that any imbalance in the currentmeasurement unit 1520 may be mitigated. In this instance, the currentmeasurement unit 1520 may be configured to determine a first transistorcomparison value based on a comparison of I_(D1) and I_(D2), the chop240 then switches the inputs to the current measurement unit 1520 andthe current measurement unit 1520 then determines a second transistorcomparison value. The transistor difference value can then be determinedbased on the first and second transistor comparison values, for exampleby taking an average or a sum of the first and second transistorcomparison values in the case where a chop 240 is not used, or by takinga difference between the first and second transistor comparison valuesin the case where a chop 240 is used.

Furthermore, whilst in the arrangements of FIGS. 2, 3 and 15, bothtransistors in the matched transistor pair 210 are selected at the sametime so their transistor on-state characteristics can be compareddirectly against each other, in an alternative implementation eachtransistor may be selected at a separate time and their transistoron-state characteristic measured. The two measurements may then becompared in order to determine the transistor difference value.

FIG. 16 shows one particular example implementation of such anarrangement. The determination unit 170 comprises a current source 1610and a selector circuit 1620 that is configured to apply a selectionpotential to a first transistor of the matched pair of transistors 1620and a non-selection potential to a second transistor of the matched pairof transistors 210, so that only the first transistor in the pair isturned on. The MUX 1630 is configured to output the source voltage ofthe first transistor to the ADC 1640 so that the ADC 1640 can measurethe transistor on-state characteristic of the first transistor, which inthis example is the source voltage. The selector circuit 1620 may thenapply a selection potential to the second transistor and apply anon-selection potential to the first transistor. The MUX 1630 thenoutputs the source voltage of the second transistor to the ADC 1640 sothat the ADC can measure the transistor on-state characteristic of thesecond transistor. The on-state characteristics of the first and secondtransistors can then be compared, for example by a PUF output unit orsome other suitable unit coupled to the ADC 1640 and configured toreceive and record the measurements of the transistor on-statecharacteristics. The operation of the selector circuit 1620 and MUX 1630may be controlled by any suitable entity, for example by a control unitin the determination unit 170. Furthermore, the skilled person willappreciate that separately selecting each transistor in a match pair oftransistors and measuring their transistor on-state characteristic maybe extended to all of the other arrangements described herein by makingsuitable changes to the configuration, such as those explained abovewith reference to FIG. 16.

FIG. 4 shows a further example configuration of the PUF apparatus 100 inaccordance with an aspect of the present disclosure. In the PUFapparatus 100 represented in FIG. 4, the PUF cell 105 comprises amatched pair of transistors 210 that are configured as source followersin the same way as FIG. 2. Furthermore, the determination unit 170comprises a first current source 232, a second current source 234 and achop 236, all of which operate as described above with reference to FIG.2. The operation of the first current source 232, second current source234 and chop 236 may be controlled, for example, but the PUF output unit310, or any other suitable module/unit.

However, in contrast to the arrangement represented in FIG. 2, thedetermination unit 170 in this example further comprises a DAC 410, theoperation of which is controlled by the PUF output unit 310, and acomparator 430. As will be appreciated from the description below, theDAC 410, PUF output unit 310 and comparator 430 are configured tooperate together as a slope converter ADC in order to compare atransistor on-state characteristic of the matched pair of transistors210. The operation of the determination unit 170 shall now be describedwith reference to FIG. 5.

The DAC 410 outputs two ‘ramp signals’—a first ramp signal 411 thatramps from +full scale to −full scale, and a second ramp signal 412 thatramps from −full scale to +full scale. The PUF output unit 310 controlsthis operation, for example by supplying an increasing/decreasingdigital counter value to the DAC 410, which the DAC 410 converts to ananalog ramp signal. To this end, the PUF output unit 310 may comprise atleast one counter that is increasing or decreasing in value. This may beseen in the diagram ‘DAC ramp signals’ in FIG. 5, which shows tworepeats of the ramp signals—one for ‘conversion 1’ and one for‘conversion 2’. The selector circuit 420 is configured to output a pairof voltage signals 422. During ‘conversion 1’, for the selected row y, afirst input signal is applied to a first transistor of the matched pairof transistors 210, comprising a first current signal from the firstcurrent source 232 and a first voltage signal from the selector circuit420. The first voltage signal is the first ramp signal 411. A secondinput signal is applied to a second transistor of the matched pair oftransistors 210, comprising a second current signal from the secondcurrent source 234 and a second voltage signal from the selector circuit420. The second voltage signal is the second ramp signal 412.

It will be appreciated that the source voltages of the matched pair oftransistors 210 should vary with the ramp signal applied to the gates ofthe transistors. The input terminals to the comparator 430 arerespectively coupled to the source terminals of the matched pair oftransistors 210. As the skilled person will appreciate, the output ofthe comparator 430 should change from low to high, or vice-versa, whenthe signal at one input terminal becomes larger than the signal at theother input terminal. With reference to FIG. 5, if the matched pair oftransistors 210 were absolutely identical, you would expect thecomparator 430 output to change substantially at the moment the two rampsignals 411 and 412 cross (i.e., substantially at the mid-point between−full scale and +full scale). However, due to random manufacturingdifferences between the two transistors, their turn-on thresholdvoltages are likely to be different, meaning that for the same gatevoltages, their gate-source voltages are likely to be different.Consequently, the moment at which the source voltages cross over and thecomparator 430 output changes is unlikely to be the same moment at whichthe ramp voltages 411 and 412 cross. This is shown in FIG. 5 by Δ₁,which is the difference between the gate voltages of the matched pair oftransistors 210 at the moment the comparator 430 output changes. Thischange in comparator 430 output may trigger the PUF output unit 310 tostore the M-bit value of the counter used to control the DAC 410. TheM-bit value of the counter at the moment that the comparator 430 outputchanges is indicative of a difference between the turn-on thresholdvoltages of the matched pair of transistors 210. This M-bit value isreferred to from here on as ‘conversion 1’.

However, conversion 1 may be affected by any mismatch between the firstand second current sources 232 and 234 and/or any inherent offsetbetween the input terminals of the comparator 430 _(x) and/or any delaysthat are within the circuit.

In some instances, these inaccuracies may be sufficiently small thatthey can be ignored. In this instance, conversion 1 may be used as thetransistor difference value that is indicative of a random manufacturingdifference between the matched pair of transistors 210, which has causeda difference in the turn-on threshold voltage/gate-source voltage of thematched pair of transistors 210. In this case, conversion 2 is notrequired at all and the PUF output may be determined based at least inpart on the transistor difference value (as described earlier withreference to FIGS. 2 and 3).

However, in other instances, any one or more of these contributions toinaccuracy may be too great to ignore, without causing an undesirablereduction in the randomness of the transistor difference value, andtherefore a reduction in the effectiveness of the PUF apparatus 100 togenerate a sufficiently random PUF value. In this case, a secondconversion can be carried out, where the input signals to the PUF cell105 are switched and, optionally, the input terminals to the comparator430 are switched.

In the second conversion, the first input signal is applied to thesecond transistor, the first input signal comprising the first currentsignal from the first current source 232 and the first voltage signalfrom the selector circuit 420. The first voltage signal is the firstramp signal 411. The second input signal is applied to the firsttransistor, the second input signal comprising a second current signalfrom the second current source 234 and a second voltage signal from theselector circuit 420. The second voltage signal is the second rampsignal 412. This switching of the current signals may be achieved by thechop circuit 236 in the same way as described earlier with reference toFIGS. 2 and 3. The switching of the voltage signals may be achieved bythe selector circuit 420 changing which of the ramp signals 411 and 422is applied to which of the pair of voltage signals 422. Optionally, thechop circuit 240 may also switch the inputs to the comparator 430,although in some instances the comparator 430 offset may be sufficientlysmall for it to be ignored and the chop circuit 240 may be omitted. Tothis end, the PUF output unit 310 may be configured to control the chopcircuit 236, the chop circuit 240 and the selector circuit 420.

FIG. 5 shows the second conversion and it can be seen that the moment atwhich the comparator 430 output changes, the difference between the rampvoltages is Δ₂. At that time, the PUF output unit 310 may be triggeredto store the M-bit count value, which is indicative of a differencebetween the turn-on threshold voltages of the matched pair oftransistors 210. This M-bit value is referred to from here on as‘conversion 2’.

The M-bit count value of conversion 1 may be expressed as:Conversion 1=ΔV _(GS)+mismatch/offset+delay+noise1

In this example, conversion 1 is a first transistor comparison value.

The M-bit count value of conversion 2 may be expressed as:Conversion 2=−ΔV _(GS)+mismatch/offset+delay+noise2

In this example, conversion 2 is a second transistor comparison value.

It can be seen that the sign of ΔV_(GS) has changed between conversion 1and conversion 2, as a result of switching the input voltage signals.Thus, if we take the difference between conversion 1 and conversion 2,we are left with:Transistor difference value=conversion 1−conversion 2=2*ΔV_(GS)+(noise1−noise2)

Therefore, by taking two conversions in this way and subtracting onefrom the other, any correlated errors and noise between the twoconversions, such as mismatch/offset and delay in the circuit, may besignificantly reduced or eliminated to the first order. Furthermore, theΔV_(GS) component has increased by 2× and low frequency components ofnoise1 and noise2 should mostly cancel each other out. Consequently, theaccuracy of the transistor difference value as a measure of thedifference between the gate-source voltages of the matched pair oftransistors 210 is increased. The PUF output may be determined based atleast in part on the transistor difference value (as described earlierwith reference to FIGS. 2 and 3), which, owing to the increase inaccuracy of the transistor difference value, may be a more reliablyrandom number.

It should be appreciated that in this example both the first voltagesignal and the second voltage signal applied to the matched pair oftransistors 210 are ramp signals, which may help to improve the commonmode rejection ratio (CMRR) of the circuit and make the measurementprocess more purely differential. However, in alternativeimplementations, only one of the first voltage and second voltagesignals may be a ramp voltage (either increasing or decreasing), withthe other voltage signal being a static reference voltage that is set toany suitable value between the upper and lower limits of the rampsignal.

In a further alternative implementation, the ADC comprising the DAC 410,comparator 430 and PUF output unit 310 may be configured as a SAR ADC,for example by virtue of the PUF output unit 310 controlling the DAC 410differently by applying digital values to the DAC 410 in accordance withthe operation of a SAR ADC, rather than in accordance with the operationof a slope ADC. In this alternative, the PUF output unit 310 may notcomprise a counter, but may instead set the digital value in any othersuitable way in accordance with the operation of a SAR ADC. Using a SARADC may help to improve the speed of the conversion, but would require aseparate DAC to be allocated to each PUF cell 105 _(x,y) in a row, sincethe DAC input for a SAR ADC cannot be shared amongst all cells in a row.

FIG. 6 shows a schematic diagram of an array of PUF cells 105 _(x,y)that are each configured in the same way as the PUF cell 105 representedin FIG. 4. As can be seen, the selector circuit 420 has Y pairs ofvoltage signals 422 _(y). As explained earlier, by setting one of thepairs of voltage signals 422 _(y) to a selection potential (which inthis example is the two ramp signals 411 and 412), all of the PUF cells105 _(x,y) in that row are selected. The other pairs of voltage signals422 _(y) output from the selector circuit 420 are held at anon-selection potential, which is below the turn-on threshold voltage ofthe matched pairs of transistors 210 _(x,y) so that the transistors inthe other rows of PUF cells 105 _(x,y) are turned off and are thereforenot selected. For each column of PUF cells 105 _(x,y) there is provideda first current source 232 _(x), a second current source 234 _(x), achop circuit 236 _(x), a further chop circuit 240 _(x) and a comparator430 _(x). The PUF output unit 310 is configured to receive the output ofeach of the comparators 430 _(x), such that for each column it may storethe counter value at the time that the respective comparator 430 _(x)output switches. The PUF output unit 430, or any other suitable unit,may control the operation of the DAC 410, the selector circuit 420, thechop circuit 236 _(x) and the further chop circuit 240 _(x), asdescribed above.

In operation, the selector circuit 420 may select a row of PUF cells 105_(x,y), for example the first row of PUF cells 105 _(x,1). A transistordifference value may be determined for each of the selected PUF cells inparallel. The selector circuit 420 may then select a different row ofPUF cells 105 _(x,y), for example the second row of PUF cells 105_(x,2). A transistor difference value may then be determined for each ofthe selected PUF cells in parallel. In this way, transistor differencevalues may be determined for all of the PUF cells 105 _(x,y), and thePUF output may then be determined by the PUF output unit 310 based onthe transistor difference values, as described earlier with respect ofFIG. 3.

In some implementations, the number of PUF cells 105 _(x,y) may exceedthe number of bits in the PUF output. In this case, during enrolment ofthe PUF apparatus 100, the transistor comparison described above may becarried out for all of the PUF cells 105 _(x,y). The PUF cells 105_(x,y) that are found to have the largest difference in turn-onthreshold voltage between the transistors may then be registered for usein determining the PUF output in the future. The remaining PUF cells 105_(x,y) may effectively be ignored from then on. By using only the PUFcells 105 _(x,y) with the largest difference in turn-on thresholdvoltage, the persistence of the PUF output may be improved, sincechanges over time in the magnitude of a difference in the transistoron-state characteristic (for example, caused by component drift,measurement noise, etc) are less likely to cause a change in which ofthe two transistors has the largest turn-on threshold voltage.

By determining the transistor difference values in parallel for the Xpairs of transistors 210 _(x,y) in a selected row, the speed ofoperation of the PUF apparatus 100 may be increased. Furthermore, eachset of first and second current sources 232 _(x) and 234 _(x), chopcircuits 236 _(x), further chop circuits 240 _(x) and ADC 250 _(x) maybe shared by a column of the PUF array, thereby reducing the number ofcomponents required and thus the overall size, cost and powerconsumption of the PUF apparatus 100. Furthermore, the determinationunit 170 need comprise only one DAC 410 and one counter (or similar) inthe PUF output unit 310, thereby maximising resource sharing across thePUF array and minimising the number of components required and thus theoverall size, cost and power consumption of the PUF apparatus 100.Consequently, the PUF apparatus 100 can be made relatively small, denseand low power.

It should be appreciated that in an alternative implementation of thePUF apparatus 100 represented in FIGS. 4 and 6, the PUF apparatus 100may be configured to determine a transistor difference value for one ormore PUF cells 105 _(x,y) based on a different transistor on-statecharacteristic, such as that described above with reference to FIG. 15.

FIG. 7 shows a further example configuration of the PUF apparatus 100 inaccordance with an aspect of the present disclosure. The PUF apparatus100 represented in FIG. 7 is very similar to that represented in FIG. 4,except that the PUF cell 105 comprises a matched pair of transistors 210that are configured as a differential pair and a single current source720 can be provided for the tail current of the differential pair.

Furthermore, the comparator 730 may be implemented differently to thecomparator 430 of FIG. 4, as explained in more detail later.

The comparator 730 is coupled to the drains of the matched pair oftransistors 210, such that the output of the comparator 730 shouldchange when one of the drain currents becomes larger than the other.Since the gate voltage of each transistor is held to the potential ofthe pair of voltages 422 and the source voltage of each transistor isheld by the current source 720, random manufacturing differences betweenthe matched pair of transistors 210 (for example, causing differences inturn-on threshold voltages, and therefore gate-source voltages) may bedetected by virtue of differences in the drain currents of the matchedpair of transistors 210. In order to determine the transistor differencevalue, two conversions may be executed as described above with referenceto FIG. 5, the only differences being that because there is a singlecurrent source 720, the first input signal comprises only a firstvoltage signal (the first ramp signal 411) and the second input signalcomprises only a second voltage signal (the second ramp signal 412), andthat the comparator 730 output changes when the drain currents of thematched pair of transistors 210 crosses over (rather than when thesource voltages cross over). Each conversion generates a transistorcomparison value that is indicative of a difference in the turn-onthreshold voltage/V_(GS) of the matched pair of transistors 210.

As explained earlier, the M-bit count value of conversion 1 may beexpressed as:Conversion 1=ΔV _(GS)+offset+delay+noise1

Conversion 1 is a first transistor comparison value and offset is theoffset of comparator 730.

The M-bit count value of conversion 2 may be expressed as:Conversion 2=−ΔV _(GS)+offset+delay+noise2

Conversion 2 is a second transistor comparison value.

As explained earlier:Transistor difference value=Conversion 1−conversion 2=2*ΔV_(GS)+(noise1−noise2)

Therefore, a transistor difference value indicative of ΔV_(GS), andtherefore indicative of random manufacturing differences, can bedetermined more accurately by mitigating the offset and delayinaccuracies. However, as explained earlier, in some implementationswhere the offset and delay are considered to be sufficiently small to beignored, the transistor difference value may be found from a singleconversion, such that conversion 1, or conversion 2, is the transistordifference value.

Furthermore, whilst in this example the first voltage signal is thefirst ramp signal 411 and the second voltage signal is the second rampsignal 412, in an alternative only one of the voltage signals may be aramp signal (either ramping up or down) and the second voltage signalmay be a fixed voltage reference, fixed to any suitable value (asdescribed earlier). In a further alternative, rather than operating as aslope ADC, the PUF output unit 310 may be configured to drive the DAC410 such that the ADC operates as an SAR ADC, as explained earlier.

The inventors have recognised that by implementing the matched pair oftransistors 210 as a differential pair, the matched pair of transistors210 may form the input transistors of the comparator 730. This may beappreciated more fully from FIG. 8.

FIG. 8 shows a schematic diagram illustrating the matched pair oftransistors 210 and the partial comparator block 830, which togetherform a full comparator. As the skilled person will appreciate, thematched pair of transistors 210 form the differential pair at the inputof the full comparator, wherein the differential input of the fullcomparator is applied to the gates of the differential pair. The skilledperson will also recognise that the transistors in the partialcomparator block 830 make up the rest of a pre-amplifier of the fullcomparator and the latch circuit completes the full comparator. Thus,the determination unit 170 in this example where the matched pair oftransistors 210 form a differential pair may be configured with both afull comparator 730 and the matched pair of transistors 210, or it maybe configured with a partial comparator block 830 and the matched pairof transistors 210.

FIG. 9 shows an example representation of an array of PUF cells 105_(x,y) in accordance with this aspect of the disclosure, wherein thepartial comparator block 830 _(x) is used. The determination of thetransistor difference value(s) and the PUF output can be understood fromthe earlier description with respect to FIGS. 4, 6 and 7. However, itcan be appreciated from FIG. 10 that by utilising the partial comparatorblock 830 _(x), two fewer transistors per column are required, since theinput differential pair of the full comparator for column x is formed bythe selected matched pair of transistors 210 _(x,y) in column x. Thisfurther reduces the overall size and power consumption of the PUFapparatus 100, thereby increasing density and reducing costs.Furthermore, it means that any comparator offset caused by the inputdifferential pair 210 of the full comparator is actually caused byΔV_(GS) and, as such, does not contribute to the ‘offset’ component of‘Conversion 1’ and ‘Conversion 2’ described above. Since fewercomponents now contribute to the undesirable ‘offset’ component (onlythe components in the partial comparator block 830, which have arelatively small influence on input referred offset), it may reduce‘offset’ to a level where it can be ignored, such that only a singleconversion may be required to determine the transistor difference value,in which case the further chop circuit 240 _(x) may be omitted. However,in some cases the offset of the partial comparator block 830 may besufficient to require the further chop circuit 240 _(x) and the twoconversions described above.

Transistor Matched Pair Layout

Example transistor layouts for the matched pair of transistors 210_(x,y) shall now be described.

The inventors have recognised gradients across a PUF cell in thethickness/doping concentration/impurities of one or more semiconductorlayers may adversely affect the randomness of the difference between thetwo transistors making up the matched transistor pair 210 _(x,y). Forexample, if the thickness of the gate oxide layer gradually increasesacross the die from one end to another, then the gate oxide thickness onone of the transistors may always be slightly greater than the othertransistor. For example, looking at FIGS. 3, 6 and 9, if the gate oxidethickness has an increasing gradient across the PUF cell array from leftto right, in each PUF cell 105 _(x,y), the transistor on the left sideof each PUF cell 105 _(x,y) is more likely to have a slightly thinnergate oxide than the transistor on the right side of each PUF cell 105_(x,y). This may skew the probably of the transistor comparison awayfrom 50:50, such that the chances of one transistor having a largertransistor on-state characteristic (such as V_(TH), or V_(GS), or I_(D))than the other transistor is no longer 50:50.

It has been determined that this effect may be reduced by designing thematched pair of transistors 210 _(x,y) to be as small as possible and asclose together as possible. Furthermore, it has also been determinedthat a so-called, ‘common centroid’ arrangement may further improvegradient rejection, thereby improving the probability of the transistorcomparison being substantially 50:50.

FIG. 10 shows an example representation transistor positioning to helpexplain a ‘common centroid’ arrangement. In FIG. 10A, the firsttransistor T_(A) and the second transistor T_(B), that together make upthe matched pair of transistors 210 _(x,y), are positioned a long wayapart. In this case, the matched pair of transistors 210 _(x,y) arelikely to be susceptible to gradients, particularly in the up/downdirection in the drawing. FIG. 10B shows a similar arrangement, butwhere the first transistor T_(A) and the second transistor T_(B) arepositioned close together. This may help to reduce the effect ofgradients, particularly in the up/down direction in the drawing.

FIG. 10C shows one example ‘common centroid’ arrangement. In thisexample, the first transistor T_(A) is made up of a first sub-transistorT_(A1) and a second sub-transistor T_(A2). The second transistor T_(B)is made up of a third sub-transistor T_(B1) and a fourth sub-transistorT_(B2). Owing to the positioning of the sub-transistors, the centroid,or centre of mass, of the first transistor T_(A) is in substantially thesame position as the centroid, or centre of mass, of the secondtransistor T_(B). Consequently, the overall effect of any linear orfirst order gradient across the PUF cell 105 _(x,y) should be evened outfor the matched pair of transistors 210 _(x,y), thereby achievinggradient rejection.

FIG. 10D shows a further example ‘common centroid’ arrangement. Again,owing to the positioning of the sub-transistors, the centroid, or centreof mass, of the first transistor T_(A) is in substantially the sameposition as the centroid, or centre of mass, of the second transistorT_(B). Consequently, the overall effect of any gradient across the PUFcell 105 _(x,y) should be evened out for the matched pair of transistors210 _(x,y), thereby achieving gradient rejection.

Details of an example ‘common centroid’ arrangement shall now bedescribed with reference to FIGS. 11-13.

FIG. 11A shows an example representation of a matched pair oftransistors 210 _(x,y). This is a simplified representation of part ofthe PUF apparatus described above with reference to FIG. 7. The firsttransistor of the matched pair of transistors 210 _(x,y) is labelledT_(A) and the second transistor of the pair is labelled T_(B). The drainvoltage of the first transistor T_(A) is labelled V_(Da) and the drainvoltage of the second transistor T_(B) is labelled V_(Db).

FIG. 11B shows an example representation of how the matched pair oftransistors 210 _(x,y) may be implemented by sub-transistors. The firsttransistor T_(A) comprises a first sub-transistor ST_(A1) and a secondsub-transistor ST_(A2). The second transistor T_(B) comprises a thirdsub-transistor ST_(B1) and a fourth sub-transistor ST_(B2).

FIG. 12 shows an example semiconductor layout of the matched pair oftransistors 210 _(x,y) represented in FIG. 11B. The matched pair oftransistors 210 _(x,y) are arranged to have a common centroidconfiguration, corresponding to that represented in FIG. 10C. A dopedwell or back gate region (for example, an n-type substrate for a p-typeFET) is represented by reference numeral 1110. The first sub-transistorST_(A1) comprises a source contact S₁ and a drain contact D₁, each ofwhich may be highly doped well regions within the semiconductorsubstrate (for example, p+ wells for a p-type FET). The firstsub-transistor ST_(A1) also comprises a gate G_(A1). The thirdsub-transistor ST_(B1) comprises a source contact S₂ and the draincontact D₁, each of which may be highly doped well regions within thesemiconductor substrate (for example, p+ wells for a p-type FET). Thus,it can be seen that the first and third sub-transistors share the draincontact D₁. The third sub-transistor ST_(B1) also comprises a gateG_(B1). The fourth sub-transistor ST_(B2) comprises the source contactS₂ and a drain contact D₂, each of which may be highly doped wellregions within the semiconductor substrate (for example, p+ wells for ap-type FET). Thus, it can be seen that the third and fourthsub-transistors share the source contact S₂. The fourth sub-transistorST_(B2) also comprises a gate G_(B2). The second sub-transistor ST_(A1)comprises a source contact S₃ and the drain contact D₂, each of whichmay be highly doped well regions within the semiconductor substrate (forexample, p+ wells for a p-type FET). Thus, it can be seen that thesecond and fourth sub-transistors share the drain contact D₂. The secondsub-transistor ST_(A2) also comprises a gate G_(A2).

By sharing source and drain contacts in this way, the matched pair oftransistors 210 _(x,y) may be made smaller, whilst still achieving acommon-centroid arrangement. Not only does this help to reduce/eliminategradient effects, but it also means that the PUF array may be moredensely packed with pairs of transistors 210 _(x,y), thereby reducingthe size of the PUF apparatus 100. For example, the semiconductor designrepresented in FIG. 12 may be fabricated to the following dimensions:

X pitch=1.66 um

Y Pitch=3.6 um

Area=5.976 um{circumflex over ( )}2

Process dimension=0.18 um

Cell area (normalised to process minimum dimension)=33.2 F{circumflexover ( )}2

Since each PUF cell 105 _(x,y) may comprise only the matched pair oftransistors 210 _(x,y), it is therefore possible to each PUF cell 105_(x,y), to achieve the dimensions identified above, whilst alsoachieving a common centroid arrangement. This means that a very small,high density PUF array may be achieved.

It should be noted that if a non-common centroid arrangement wereinstead used, it would be possible to halve the Y pitch and achieve aPUF cell 105 _(x,y) of half the area identified above. Whilst such anarrangement would not have the benefits of the common centroidarrangement, it may result in an even smaller, higher density PUF array.

FIG. 13 shows an example representation of how the transistor layout ofFIG. 12 may be used to create an array of PUF cells 105 _(x,y). The PUFarray represented in FIG. 13 corresponds with that represented in FIG.9. As can be seen, adjacent pairs of transistors 210 _(x,y) in a columnare arranged to share source contacts. For example, the source contactof the second sub-transistor ST_(A2) in the transistor pair 210 _(x,y)is shared with the source contact of the first sub-transistor ST_(A1) inthe transistor pair 210 _(x, y+1). This not only increases the densityof packing of the PUF cells 105 _(x,y), but it also reduces the numberof interconnections required to the current source 720 _(x) in eachcolumn, thereby simplifying manufacturing and reducing wiring/viacomplexity. It will be appreciated that whilst in this example adjacentPUF cells 105 _(x,y) share source contacts, in alternativeconfigurations (for example, one corresponding to the arrangementrepresented in FIG. 3) they may alternatively share drain contacts.Thus, adjacent pairs of transistors 210 _(x,y) in a column may bearranged to share channel contacts, either source or drain.

In the layout represented in FIGS. 12 and 13, the sub-transistors areconfigured such that when the first transistor T_(A) is conductingcurrent, a channel current in the first sub-transistor ST_(A1) flowsfrom drain D₁ to source S₁ in a first direction in the semiconductor.This first direction appears as ‘upwards’ in the representation shown inFIG. 12. A channel current in the second sub-transistor ST_(A2) flowsfrom drain D₂ to source S₃ in a second direction in the semiconductor,which is substantially opposite to the first direction. This seconddirection appears as ‘downwards’ in the representation shown in FIG. 12.When the second transistor T_(B) is conducting current, a channelcurrent in the third sub-transistor ST_(B1) flows from D₁ to source S₂in the second direction and a channel current in the fourthsub-transistor ST_(B2) flows from drain D₂ to source S₂ in the firstdirection (although it will be appreciated that in an alternative, thepositions of the third sub-transistor ST_(B1) and fourth sub-transistorST_(B2) may be switched, such that the channel current in the thirdsub-transistor ST_(B1) flows in the first direction and the channelcurrent in the fourth sub-transistor ST_(B2) flows in the seconddirection.

By arranging the sub-transistors so that the channel current in eachsub-transistor making up a transistor flows in substantially oppositedirections, gradient effects may be further cancelled out, therebyimproving gradient rejection and, therefore, the randomness of thetransistor difference value.

Whist FIGS. 12 and 13 show one particular example of how thesub-transistors may be arranged to achieve common centroid, channelcontact sharing and substantially opposite channel current directions,the sub-transistors may be arranged differently and still achieve someor all of these effects. For example, the arrangements may differ fordifference types of transistor (such as n-type or p-type, etc) and/orthey may be arranged in a different common-centroid configuration, suchas that of FIG. 10D.

FIG. 17 shows a graphical representation of a method for determining aPUF output using a plurality of PUF cells. This method may be performedby any of the configurations of determination unit 170 and PUF cells 105_(x,y) disclosed above.

In S1710, one or more PUF cells 105 _(x,y) are selected, for example byapplying a selection potential to the selection mechanism of those oneor more PUF cells 105 _(x,y). In some instances, one PUF cell 105 _(x,y)at a time may be selected and in other instances a plurality of PUFcells 105 _(x,y) may be selected at the same time (for example, some orall of the PUF cells in a particular row of an array of PUF cells).

In S1720, for each selected PUF cell 105 _(x,y), a transistor differencevalue is determined based at least in part on a comparison of anon-state characteristic of the matched pair of transistors 210 _(x,y) inthe selected PUF cell(s) 105 _(x,y), wherein the transistor differencevalue is indicative of a random manufacturing difference between thematched pair of transistors 210 _(x,y) in the selected PUF cell(s) 105_(x,y).

Optionally, if there is a further PUF cell(s) 105 _(x,y) still to beselected and to have a transistor difference value determined, themethod may return to S1710 to select that PUF cell(s) 105 _(x,y) andthen determine the corresponding transistor difference value. Forexample, this may be moving onto the next row in a PUF array after thetransistor difference values have been determined for the preceding row.Once all of the PUF cells 105 _(x,y) have been selected and theirtransistor difference values determined, the method may then proceed toS1730. Alternatively, for example where all PUF cells 105 _(x,y) can beselected and their transistor difference values determined in a singleiteration of S1710 and S1720, the method may always proceed directlyfrom S1720 to S1730.

In S1730, the PUF output is determined based at least in part on the atleast one determined transistor difference value, as explained earlier.

The skilled person will readily appreciate that various alterations ormodifications may be made to the above described aspects of thedisclosure without departing from the scope of the disclosure.

For example, whilst in all of the above disclosed aspects each PUF cell105 _(x,y) comprises only the matched pair of transistors 210 _(x,y),which function as both the selection mechanism and the transistors to becompared to determine the transistor difference value, in an alternativeimplementation the PUF cells 105 _(x,y) may comprise more than twotransistors. For example, they may comprise the matched pair oftransistors 210 _(x,y), and also one or more transistors configured as aselection mechanism.

FIG. 14 shows a schematic representation of an example PUF cell 105_(x,y) comprising selection transistors 1410 _(x,y), which function as aselection mechanism. The selection transistors 1410 _(x,y) in thisexample comprise two p-type FETs. The PUF cell 105 _(x,y) may beselected by applying a selection potential to select the PUF cell 105_(x,y), wherein the selection potential is a potential sufficient toturn-on the selection transistors 1410 _(x,y). Any PUF cells 105 _(x,y)that are not to be selected at a particular time may have anon-selection potential applied to the selection transistors 1410 _(x,y)such that the selection transistors 1410 _(x,y) are turned off.Therefore, to determine a transistor difference value from a particularPUF cells 105 _(x,y), a selection potential is applied to ‘select’ (forexample, by the selector circuit 420) and, separately, first and secondsignals are applied to the matched pair of transistors 210 _(x,y) (forexample, by current sources and/or the selector circuit 420, or someother suitable circuit/unit). In an alternative, there may be only asingle selection transistor per PUF cell 105 _(x,y), for example coupledbetween the sources of the matched pair of transistors 210 and thecurrent source 720 in the arrangement represented in FIG. 8.Furthermore, whilst the selection transistors 1410 _(x,y) arerepresented in combination with the matched pair of transistors 210_(x,y) configured as a differential pair, it should be appreciated thatselection transistors 1410 _(x,y) may be used in combination with anyconfiguration of the matched pair of transistors 210 _(x,y) (forexample, in combination with that of FIG. 2 or 4).

The selection transistors 1410 _(x,y) are of the same transistor type asthe matched pair of transistors 210 _(x,y), such that plurality oftransistors in a PUF cell 105 _(x,y) are all of the same transistortype. This is not to mean that they are all of identical design, butthat they are all n-type, or all p-type. By doing so, the plurality oftransistors in the PUF cell 105 _(x,y) may be more densely packed,thereby reducing the overall size of the PUF apparatus and also reducingthe gradient issues described above.

The term ‘coupled’, used throughout this disclosure, encompasses bothdirect connections between components and indirect connections, whereinone or more intermediate component may be present in the coupling.

The array of PUF cells disclosed herein may be of any size and shape,for example with only one row and many columns, or vice-versa.Furthermore, whilst the present disclosure is generally in the contextof an array of PUF cells, it will be appreciated that the plurality ofPUF cells may be arranged in any suitable fashion and not necessarily asan array.

The invention claimed is:
 1. A Physically Unclonable Function, PUF,apparatus comprising: a plurality of PUF cells, each PUF cellcomprising: a plurality of transistors, wherein the plurality oftransistors comprises: a matched pair of transistors for transistoron-state characteristic comparison, and a selection mechanism forselecting the PUF cell, and wherein the plurality of transistors in eachPUF cell are all of a same transistor type; and a determination unitconfigured to: select at least one of the plurality of PUF cells usingthe selection mechanism in each of the at least one of the plurality ofPUF cells; for each selected PUF cell, determine a transistor differencevalue based at least in part on a comparison of an on-statecharacteristic of the matched pair of transistors in the selected PUFcell, wherein the transistor difference value is indicative of a randommanufacturing difference between the matched pair of transistors in theselected PUF cell; and determine a PUF output based at least in part onthe determined transistor difference value.
 2. The apparatus of claim 1,wherein the selection mechanism comprises gate terminals of the matchedpair of transistors, and wherein the determination unit is configured toselect a PUF cell by applying a selection potential to one or more ofthe gate terminals of the matched pair of transistors in the PUF cell.3. The apparatus of claim 1, wherein the selection mechanism comprisesone or more selection transistors coupled to the matched pair oftransistors, and wherein the determination unit is configured to selecta PUF cell by applying a selection potential to the one or moreselection transistors to control an operation of the one or moreselection transistors.
 4. The apparatus of claim 1, wherein thecomparison of the on-state characteristic of the matched pair oftransistors comprises a comparison of a gate-source voltage of thematched pair of transistors.
 5. The apparatus of claim 1, wherein thedetermination unit is configured to determine the transistor differencevalue for the selected PUF cell by: (a) applying a first input signal toa first transistor of the matched pair of transistors; applying a secondinput signal to a second transistor of the matched pair of transistors;and determining a first transistor comparison value by comparing theon-state characteristic of the first transistor when the first inputsignal is applied against the on-state characteristic of the secondtransistor when the second input signal is applied; then (b) applyingthe second input signal to the first transistor of the matched pair oftransistors; applying the first input signal to the second transistor ofthe matched pair of transistors; and determining a second transistorcomparison value by comparing the on-state characteristic of the firsttransistor when the second input signal is applied against the on-statecharacteristic of the second transistor when the first input signal isapplied; and then (c) determining the transistor difference value basedon the first transistor comparison value and the second transistorcomparison value.
 6. The apparatus of claim 5, wherein the determinationunit is configured to: in (a), simultaneously apply the first inputsignal to the first transistor and the second input signal to the secondtransistor; and in (b), simultaneously apply the second input signal tothe first transistor and the first input signal to the secondtransistor.
 7. The apparatus of claim 5, wherein the determination unitfurther comprises: at least one first current source configured tooutput a first current signal; and a second current source configured tooutput a second current signal; wherein the first input signal comprisesthe first current signal and the second input signal comprises thesecond current signal.
 8. The apparatus of claim 5, wherein the firstinput signal comprises a first voltage signal and the second inputsignal comprises a second voltage signal.
 9. The apparatus of claim 8,wherein at least one of the first voltage signal and the second voltagesignal vary with time.
 10. The apparatus of claim 8, wherein thedetermination unit is configured to: during determination of the firsttransistor comparison value for the selected PUF cell, apply the firstvoltage signal to a gate terminal of the first transistor and apply thesecond voltage signal to a gate terminal of the second transistor; andduring determination of the second transistor comparison value for theselected PUF cell, apply the second voltage signal to the gate terminalof the first transistor and apply the first voltage signal to the gateterminal of the second transistor so as also to select the PUF cell. 11.A Physically Unclonable Function, PUF, apparatus comprising: a pluralityof PUF cells, a first PUF cell of the plurality of PUF cells comprisinga matched pair of transistors having gate terminals representing aselection mechanism of the matched pair of transistors; and adetermination unit configured to: select the first PUF cell using theselection mechanism of the first PUF cell; for the first PUF cell,determine a transistor difference value based at least in part on acomparison of an on-state characteristic of the matched pair oftransistors in the first PUF cell, wherein the transistor differencevalue is indicative of a random manufacturing difference between thematched pair of transistors in the first PUF cell; and determine a PUFoutput based at least in part on the transistor difference value. 12.The apparatus of claim 11, wherein the matched pair of transistors areconfigured as a differential pair, and wherein the matched pair oftransistors form an input of a comparator.
 13. The apparatus of claim12, wherein the transistor difference value comprises a digital valueindicative of the random manufacturing difference between the matchedpair of transistors, and wherein the determination unit comprises anAnalog-to-Digital converter for use in determining the transistordifference value, and wherein the Analog-to-Digital converter comprisesthe comparator.
 14. The apparatus of claim 11, wherein the matched pairof transistors comprises a first transistor and a second transistor, andwherein the first transistor comprises a first sub-transistor and asecond sub-transistor, and wherein the second transistor comprises athird sub-transistor and a fourth sub-transistor, and wherein the firstsub-transistor, the second sub-transistor, the third sub-transistor, andthe fourth sub-transistor are arranged in a semiconductor layout suchthat a centre of mass of the first transistor is substantially the sameas a centre of mass of the second transistor.
 15. The apparatus of claim14, wherein the first sub-transistor, the second sub-transistor, thethird sub-transistor and the fourth sub-transistor are arranged in thesemiconductor layout such that: when the first transistor is conductingcurrent, a channel current in the first sub-transistor flows in a firstdirection in a semiconductor in which the first and second transistorsare formed and a channel current in the second sub-transistor flows in asecond direction in the semiconductor, and when the second transistor isconducting current, a channel current in one of the third sub-transistoror the fourth sub-transistor flows in the first direction and a channelcurrent in the other of the third sub-transistor or the fourthsub-transistor flows in the second direction, and wherein the firstdirection and the second direction are substantially opposite spatialdirections in the semiconductor layout.
 16. The apparatus of claim 14,wherein the semiconductor layout of the matched pair of transistors isarranged such that the first sub-transistor and the third sub-transistorshare a drain terminal and the second sub-transistor and the fourthsub-transistor share a further drain terminal.
 17. A method fordetermining a Physically Unclonable Function, PUF, output using aplurality of PUF cells each comprising a plurality of transistors of asame transistor type, the plurality of transistors comprising a matchedpair of transistors and a selection mechanism for selecting the PUFcell, the method comprising: selecting one or more PUF cells using theselection mechanism in each of the plurality of PUF cells; for eachselected PUF cell, determining a transistor difference value based atleast in part on a comparison of an on-state characteristic of thematched pair of transistors in the selected PUF cell, wherein thetransistor difference value is indicative of a random manufacturingdifference between the matched pair of transistors in the selected PUFcell; and determining the PUF output based at least in part on the atleast one determined transistor difference value.
 18. The method ofclaim 17, wherein determining the transistor difference value for theselected PUF cell comprises: applying a first input signal and a secondinput signal to a first transistor of the matched pair of transistorsand a second transistor of the matched pair of transistors respectively;determining a first transistor comparison value by comparing theon-state characteristic of the matched pair of transistors; applying thefirst input signal and the second input signal to the second transistorand the first transistor respectively; determining a second transistorcomparison value by comparing the on-state characteristic of the matchedpair of transistors; and determining the transistor difference valuebased on a difference between the first transistor comparison value andthe second transistor comparison value.
 19. The method of claim 18,wherein the first input signal comprises a first current and/or a firstvoltage signal, and wherein the second input signal comprises a secondcurrent and/or a second voltage signal.
 20. The method of claim 18,wherein selecting a PUF cell comprises applying a selection potential toone or more gate terminals of the matched pair of transistors in the PUFcell.